MF 135 3 cylinder Perkins motor. The engine sounds to be missing when under no load; under load she sounds to be firing satisfactorily. The injectors have been serviced and are said to be fine. The

Are you sure this is a 354 engine? I can only find reference to that series of engines as straight 6 Diesel.
Engine layout is fairly standard. Cylinder 1 is nearest the pulleys and belts. The firing order will possibly depend on the fuel type, series or version of the engine you have.
I have attached a website that will help you find the engine serial number on the engine block. This will give you the series code number making it easier to identify what detail you need.
https://shop.perkins.com/support/identify-your-engine

Perkins aren't my favourite engines - some were fairly good hard working and reliable but some were awful. Shelvoke and Drewry (SD) used Perkins and I have never been in a noisier vehicle. My biggest grouch about them was they never used a single bolt where three smaller bolts would do the job - the pressed steel covers never seemed quite up to the task of keeping oil inside, the cylinder heads were slender to say the least and manifolds seemed to hang on more by magic than any substantial mechanical method.
The 4.300 is now getting on in years...

Any engine can be made to fit into almost anything depending on the engineering capabilities of those who are carrying out the conversion.
The important thing about any conversion is to ensure the replacement engine will be able to satisfactorily do the work, especially when being fitted to a work-horse. Studying the torque and power output graphs of the former and proposed replacement and hopefully finding them similar at similar speeds should be a priority.

It should be borne in mind two identical diesel engines can have very different characteristics depending on the injection equipment setup. There is a world of difference between the setup for a truck engine intended for local town and country deliveries and a full-rated truck or coach engine intended for main road work.
Replacing the injection pump and injectors for a different setup is an expensive business...

Without cranking it, can you take the air filter off and see the throttle plate move as the throttle is moved ?
If someone else cranks it, can you be at the carb and move the carb throttle directly at the carb and control the rpm ?
If so, check your throttle rod for slack, missing spring/connection, something broken.
Sounds like the carb has nothing stopping the throttle from being sucked full open.

3 cylinder Perkin diesels were used for a long period of time in MF units
the mPN is HTS0391- alternate numbers -3639020M1
any accredited diesel specialist shop will be able to get you one or be able to repair and recalibrate your unit
you can mention that it is out of a MF tractor but the details that you want are a 3 cylinder Perkins engine
The original brand is CAV but there are other makes available

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[PDF]Perkins 4-154 Shop Manual

www.kp44.org/ftp/Perkins_4-154_Shop_Manual.pdf
88 Perkins. Engines workshop manual. 4.154. PRINTED lN U.S.A. .... removal, dismantling, assembly or refitting of a part is straightforward ... The ENGINE NUMBER is located on the cylinder ... starter motor, air cleaner, but without clutch. lb kg.

Reliability built into starter motors - Perkins Engines

www.perkins.com/en_GB/.../starter-motors.html

Perkins EnginesYou can rest assured that your genuine replacement starter motor will work ... 4 Cylinder · 6 Cylinder ... You can learn more about these cookies and general information about how to change your cookie settings by visiting our Privacy and Cookies page. ... This need for dependability is why we test each of our starter motors.

Sounds to me that you have a cylinder miss fire. Chrysler products generally set a code when a miss fire is detected. Does the shaking go away under a load (while driving) ? If the miss is always there I would focus on the ignition system and look for any vacuum leaks around the intake manifold area .

indicates injector problems and possible low fuel pressure
run the fault codes to check for EVAP and blocked cat converters

You didn't mention what kind of car you have or the engine size, but if it is a GM 4 cylinder engine, the #1 and #4 plugs are fired by the same coil. I would suspect a coil as the problem.

Get a scanner on it. You save time AND MONEY.

timing could be off and still start most likely bank 1 may have jumped a tooth 135 is on bank 1